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View Full Version : Capella (...losing my marbles?)



Buttercup
2015-Jan-17, 09:37 PM
If I'd previously known (probably did - it's difficult to think I didn't, at some point, know this in the past) that Capella is actually two stars, I apparently forgot! :eh:

http://earthsky.org/brightest-stars/capella-is-the-stellar-beacon-of-auriga-the-charioteer?utm_content=buffercc9ab&utm_medium=social&utm_source=twitter.com&utm_campaign=buffer

That article just came into my Twitter feed, and I'm like...wow, really? :o

And feel dumb (and older).

Who else here has experienced a similar "brain burp"?

DaveC426913
2015-Jan-18, 12:25 AM
This is why one makes the distinction - when referring to only one of them - as a capella.

:D

swampyankee
2015-Jan-18, 04:06 AM
This is why one makes the distinction - when referring to only one of them - as a capella.

:D

To the moderators:

How bad does a pun have to be to warrant sanctions?

Swift
2015-Jan-18, 04:32 AM
To the moderators:

How bad does a pun have to be to warrant sanctions?
I think I've demonstrated repeatedly that I'm the wrong person to ask for relief from puns.

DaveC426913 is singing my song. ;)

swampyankee
2015-Jan-18, 04:47 AM
I think I've demonstrated repeatedly that I'm the wrong person to ask for relief from puns.

DaveC426913 is singing my song. ;)

I wasn't asking for relief. I was asking for permission.

Buttercup
2015-Jan-18, 01:33 PM
This is why one makes the distinction - when referring to only one of them - as a capella.

:D

Ha ha ha. :)

DonM435
2015-Jan-18, 05:11 PM
Wouldn't one of 'em be a capellum?

Noclevername
2015-Jan-19, 09:42 AM
That's what I asked the hat check lady: "Please find my cap, Ella."

Ken G
2015-Jan-19, 11:18 PM
If I'd previously known (probably did - it's difficult to think I didn't, at some point, know this in the past) that Capella is actually two stars, I apparently forgot! :eh:

http://earthsky.org/brightest-stars/capella-is-the-stellar-beacon-of-auriga-the-charioteer?utm_content=buffercc9ab&utm_medium=social&utm_source=twitter.com&utm_campaign=buffer

Just mentioning that if anyone follows that link to its science explanation, you are going to be subjected to a common untruth that really needs to be stamped out whereever it persists. Capella involves two giant stars, so are evolved stars that are at a more advanced stage of their life. The article tries to explain why this happens faster for more massive stars, but misses the point entirely. It says:
"This is because more massive stars have higher internal pressures, which causes them to burn their nuclear fuel faster and to have shorter lifespans."
That is utter baloney. More massive main-sequence stars are lower pressure objects, and their higher luminosity has nothing at all to do with their lower pressure, and their luminosity is not set by their fusion rate. The higher luminosity is because they are larger leaky buckets of light than are lower mass stars like the Sun, period. Their fusion rate is higher because it is self-regulated to replace the heat that leaks out. Their pressure is lower because they don't need to contract as much before they start fusing hydrogen, which is also why they are a bit larger. Of course, the stars in Capella are larger still, because they have big puffy convective envelopes, typical of giants. Just saying.

George
2015-Jan-20, 04:26 PM
... The higher luminosity is because they are larger leaky buckets of light than are lower mass stars like the Sun, period. Their fusion rate is higher because it is self-regulated to replace the heat that leaks out. Their pressure is lower because they don't need to contract as much before they start fusing hydrogen, which is also why they are a bit larger. Of course, the stars in Capella are larger still, because they have big puffy convective envelopes, typical of giants. Just saying.
I feel capelled to ask...

What is the leakiness? Is the energy transfer due to higher core temperatures the key, or is the greater surface area more the answer?

George
2015-Jan-20, 04:29 PM
To the moderators:

How bad does a pun have to be to warrant sanctions?

There should be rewards for good puns, rare though they be.

Noclevername
2015-Jan-20, 04:34 PM
There should be rewards for good puns, rare though they be.

I've never seen one. Do they really exist?

George
2015-Jan-20, 05:05 PM
I've never seen one. Do they really exist? Yep, both of them are impressive.

Hornblower
2015-Jan-20, 05:10 PM
I feel capelled to ask...

What is the leakiness? Is the energy transfer due to higher core temperatures the key, or is the greater surface area more the answer?
I am no expert, but I think it is a double whammy with a combination of greater photosphere area and greater transparency of the rarefied envelope.

Ken G
2015-Jan-20, 06:42 PM
What is the leakiness? Is the energy transfer due to higher core temperatures the key, or is the greater surface area more the answer?It depends on how accurate you want your description to be, but you can get a very simple (and quite crude, I admit) answer by assuming the dominant opacity is always just free electrons, so that doesn't care what the temperature is. What does care a lot about temperature is the radiative energy density, which is probably what you are asking about, and that cannot be completely ignored as an important factor, but most main-sequence stars have pretty close to the same core temperature, so that turns out to not be such a key factor. What matters most is the diffusion time (the "leakiness" of the bucket) and the size of the star (the size of the bucket). It turns out that if you make these crude simplifications, all main-sequence stars leak out their light in about the same amount of time (roughly a hundred thousand years, typically), so in that sense the "leakiness" is more or less the same for all of them. What really varies is the size of the bucket, because although they are all called "dwarfs", the larger mass ones are quite a bit bigger, so contain a lot more light to leak out-- that's the main reason they are more luminous.

George
2015-Jan-20, 09:43 PM
It depends on how accurate you want your description to be, but you can get a very simple (and quite crude, I admit) answer by assuming the dominant opacity is always just free electrons, so that doesn't care what the temperature is. What does care a lot about temperature is the radiative energy density, which is probably what you are asking about, and that cannot be completely ignored as an important factor, but most main-sequence stars have pretty close to the same core temperature, so that turns out to not be such a key factor. What matters most is the diffusion time (the "leakiness" of the bucket) and the size of the star (the size of the bucket). It turns out that if you make these crude simplifications, all main-sequence stars leak out their light in about the same amount of time (roughly a hundred thousand years, typically), so in that sense the "leakiness" is more or less the same for all of them. What really varies is the size of the bucket, because although they are all called "dwarfs", the larger mass ones are quite a bit bigger, so contain a lot more light to leak out-- that's the main reason they are more luminous. That makes sense to me given that heat transfer (conductive at least) is more of a linear relationship with radii but surface area is a square relationship.

Wouldn't the larger convective zones, as a percent of their radius, of more massive stars contribute to greater transfer as well?

Ken G
2015-Jan-21, 01:29 AM
Wouldn't the larger convective zones, as a percent of their radius, of more massive stars contribute to greater transfer as well?That's a tricky question, and convection certainly ruins my simple picture. But the simple picture still succeeds fairly well, so this suggests that convection, even in massive stars, is not the primary determiner of the heat transport timescale. I believe what happens is that convection carries a relatively small fraction of the energy flux, just enough to make sure the radiative forces are not too high (radiative forces depend on the radiation flux, so if convection reduces the need for radiative flux, it reduces the radiative forces too). Since the radiative forces are not crazy high anyway, the conduction never needs to be the dominant way that energy flux gets around in a massive star-- it's still primarily radiative diffusion (which is a lot like heat conduction, as you say).

George
2015-Jan-21, 01:55 PM
That's a tricky question, and convection certainly ruins my simple picture. But the simple picture still succeeds fairly well, so this suggests that convection, even in massive stars, is not the primary determiner of the heat transport timescale. I believe what happens is that convection carries a relatively small fraction of the energy flux, just enough to make sure the radiative forces are not too high (radiative forces depend on the radiation flux, so if convection reduces the need for radiative flux, it reduces the radiative forces too). Since the radiative forces are not crazy high anyway, the conduction never needs to be the dominant way that energy flux gets around in a massive star-- it's still primarily radiative diffusion (which is a lot like heat conduction, as you say). Ok, and your point, I think, is supported by the fact that in order to have a much larger convective zone necessarily diminishes the size of the radiative transfer interaction region, thus explaining your reduced radiative transfer. Unless the coefficient of conductivity, assuming this term exists for stellar physics, of the radiative zone differs much for different masses of stars, then it makes sense. Of course, the temperature gradient within the radiative zone would be greater since these cores run hotter, but I am guessing the boundary area has the greater say in total transfer.

Ken G
2015-Jan-22, 05:46 AM
The cores don't run much hotter, maybe a factor of 2 at most-- so that's a relatively small effect, though certainly not negligible.

George
2015-Jan-22, 03:51 PM
The cores don't run much hotter, maybe a factor of 2 at most-- so that's a relatively small effect, though certainly not negligible. But double the temperature and you have 16x the radiation. Perhaps the "radiative zone" label has me ignoring conductance far too much.

Ken G
2015-Jan-22, 04:52 PM
But double the temperature and you have 16x the radiation. Perhaps the "radiative zone" label has me ignoring conductance far too much.Yes, the temperature is a rather sensitive variable, but only a factor of 2 increase in central temperature would get us from our Sun to a star 1000 times more luminous. Or, for stellar masses from 10 to 30 times our Sun, the central temperature only ranges from 3.1 million to 3.6 million K, while the luminosity increases by almost 50. The main reason the core temperature doesn't matter much, despite your completely valid point that the radiation density is very sensitive to temperature, is that to get higher temperature also requires that the star has to contract more, and that reduces its volume. So if you take the product of the radiation density times the volume that holds that radiation, the result is only proportional to temperature, and that's not a very sensitive dependence. (In fact, it cancels out completely when you also include the increase in density when the volume drops, which slows the escape of the light.)

trinitree88
2015-Feb-03, 06:40 PM
It's not just convective leakiness, it's the differentiation of isotope concentrations in the layers of massive stars. Essentially onion-like spheres develop as the stars run through their fusion options from H to He to C to N to O.on up. Burning fuels heavier than H results in more fuel required per Mev of energy generated per fusion. But, some energy is carried away as neutrinos in every fusion, too. So as the star switches fuels in the core, it burns it faster and faster to maintain thermal equilibium. But that leaks ever more energy away not as photons ,but invisible neutrinos. That produces yet greater energy losses. So even though the star contracts, heats up and radiates away more energy as the Stefan-Boltzmann Law says it should...it at the same time increases its neutrino leakage.

Ken G
2015-Feb-03, 09:18 PM
It's not just convective leakiness, it's the differentiation of isotope concentrations in the layers of massive stars. Essentially onion-like spheres develop as the stars run through their fusion options from H to He to C to N to O.on up.Yes but that's just a detail. Notice that the luminosity of a 10 solar mass star does not change hardly at all from pre-main-sequence, through main sequence, and into advanced stages of evolution. The onion skins are changing dramatically all that time, but a reasonable understanding of the luminosity can be achieved without reference to those details.


So as the star switches fuels in the core, it burns it faster and faster to maintain thermal equilibium. But that leaks ever more energy away not as photons ,but invisible neutrinos. Good point, but all this means is, you have to account for all the heat that is leaking out, not just the photons. The point is still, the fusion rate does not set any of that, it is always the rate of heat leakage that sets the fusion rate-- even if you have neutrinos as part of the energy escape process.